---
language: lmo
language_name: Lombard
language_family: romance_galloitalic
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-romance_galloitalic
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 3.475
  - name: best_isotropy
    type: isotropy
    value: 0.8136
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Lombard - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lombard** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

![Performance Dashboard](visualizations/performance_dashboard.png)

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 2.899x | 2.90 | 0.1988% | 276,191 |
| **16k** | 3.111x | 3.11 | 0.2133% | 257,402 |
| **32k** | 3.306x | 3.31 | 0.2267% | 242,211 |
| **64k** | 3.475x 🏆 | 3.48 | 0.2382% | 230,431 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `a l'è un comun de la Cechia, part de la Moravia de Sota e del distret de Hodonín...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+18 more)` | 28 |
| 16k | `▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)` | 26 |
| 32k | `▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)` | 26 |
| 64k | `▁a ▁l ' è ▁un ▁comun ▁de ▁la ▁cechia , ... (+16 more)` | 26 |

**Sample 2:** `El 872 a l'è 'n ann del secol quell de noeuv. Cossa l'è sucedud Chi l'è che l'è ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)` | 43 |
| 16k | `▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)` | 43 |
| 32k | `▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)` | 43 |
| 64k | `▁el ▁ 8 7 2 ▁a ▁l ' è ▁' ... (+33 more)` | 43 |

**Sample 3:** `Superfice: 6.334 km² Popolazzion (ISTAT 606.413 ab. Densità: 96 ab./km² Numer de...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+50 more)` | 60 |
| 16k | `▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+49 more)` | 59 |
| 32k | `▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+48 more)` | 58 |
| 64k | `▁superfice : ▁ 6 . 3 3 4 ▁km 2 ... (+48 more)` | 58 |


### Key Findings

- **Best Compression:** 64k achieves 3.475x compression
- **Lowest UNK Rate:** 8k with 0.1988% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 7,760 | 12.92 | 122,388 | 29.0% | 53.4% |
| **2-gram** | Subword | 268 🏆 | 8.07 | 6,535 | 68.2% | 98.7% |
| **3-gram** | Word | 14,354 | 13.81 | 199,723 | 22.6% | 48.6% |
| **3-gram** | Subword | 2,089 | 11.03 | 52,666 | 30.7% | 72.9% |
| **4-gram** | Word | 20,963 | 14.36 | 321,119 | 20.2% | 45.6% |
| **4-gram** | Subword | 10,897 | 13.41 | 280,505 | 17.5% | 44.7% |
| **5-gram** | Word | 15,543 | 13.92 | 228,095 | 20.6% | 47.3% |
| **5-gram** | Subword | 37,324 | 15.19 | 760,735 | 11.8% | 32.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l è` | 175,964 |
| 2 | `de la` | 121,062 |
| 3 | `a l` | 80,762 |
| 4 | `alter proget` | 33,969 |
| 5 | `de l` | 33,487 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l è` | 71,526 |
| 2 | `l è un` | 32,278 |
| 3 | `è un comun` | 23,691 |
| 4 | `l è n` | 19,224 |
| 5 | `el g ha` | 18,949 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l è un` | 30,858 |
| 2 | `l è un comun` | 23,691 |
| 3 | `è un comun de` | 15,254 |
| 4 | `un comun de la` | 15,236 |
| 5 | `l è n cümü` | 14,678 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l è un comun` | 23,684 |
| 2 | `l è un comun de` | 15,254 |
| 3 | `è un comun de la` | 15,236 |
| 4 | `cont una popolazzion de abitant` | 13,027 |
| 5 | `una popolazzion de abitant riferiment` | 12,935 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 1,432,799 |
| 2 | `_ d` | 1,057,415 |
| 3 | `e _` | 1,006,725 |
| 4 | `d e` | 886,199 |
| 5 | `_ l` | 709,001 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 789,525 |
| 2 | `d e _` | 528,733 |
| 3 | `e l _` | 383,347 |
| 4 | `l a _` | 338,250 |
| 5 | `_ l a` | 295,669 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 515,677 |
| 2 | `_ l a _` | 273,207 |
| 3 | `_ d e l` | 205,525 |
| 4 | `d e l _` | 203,248 |
| 5 | `d e _ l` | 169,714 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e l _` | 198,355 |
| 2 | `_ d e _ l` | 168,983 |
| 3 | `_ l ' è _` | 164,316 |
| 4 | `e _ l a _` | 145,472 |
| 5 | `d e _ l a` | 122,850 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 268
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~33% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 0.8496 | 1.802 | 5.71 | 320,846 | 15.0% |
| **1** | Subword | 0.9820 | 1.975 | 7.44 | 2,274 | 1.8% |
| **2** | Word | 0.3082 | 1.238 | 1.84 | 1,817,237 | 69.2% |
| **2** | Subword | 0.9539 | 1.937 | 6.24 | 16,914 | 4.6% |
| **3** | Word | 0.1317 | 1.096 | 1.27 | 3,319,649 | 86.8% |
| **3** | Subword | 0.8409 | 1.791 | 4.52 | 105,502 | 15.9% |
| **4** | Word | 0.0581 🏆 | 1.041 | 1.10 | 4,172,728 | 94.2% |
| **4** | Subword | 0.7003 | 1.625 | 3.13 | 476,503 | 30.0% |

### Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

**Context Size 1:**

1. `de bourg en fransés arrondissements e in del comun del regn d abitant riferiment lista di`
2. `l è staa fat tort che la u s cieta del dipartimènt de 215 alter proget`
3. `la stiria waidhofen an und freude ich dich dass dese en g ha na popolasiù de`

**Context Size 2:**

1. `l è de 4 23 test immanuel casto musega keen horror vacui feat romina falconi che a`
2. `de la serie a l éra csì trascüra e csì da póch che federìco i el re`
3. `a l è iniziàa in del pleistocene poeu soeu poeu giò 3 milion de alber qe l`

**Context Size 3:**

1. `a l è un comun di isole balear cont una popolazzion de abitant riferiment hacienda es alter proget`
2. `l è un paes de l asia del pakistan`
3. `è un comun del distret de hradec králové e del distret de jura nord vaudois in del canton`

**Context Size 4:**

1. `a l è un cumün svizzer del canton türgovia la süperfiss del teritori del cumün l è de 2`
2. `l è un comun del distret de prešov in la region de trnava ligam de foeura sit ofizzial alter`
3. `è un comun de la provincia de noara giamò in del el tö part a una manifestaziun ligada ai`


### Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

**Context Size 1:**

1. `_sò_denal'ètetom`
2. `a_str_mü_dinteme`
3. `essöva_gàn_m_d,_`

**Context Size 2:**

1. `a_giù_doregia_l'è`
2. `_denaa_a_de_abeci`
3. `e_imèntù_del_noli`

**Context Size 3:**

1. `_de_15_mederàl_bib`
2. `de_altèsa_movincia`
3. `el_gh'era,_elegh_u`

**Context Size 4:**

1. `_de_l'onda_dentan_d`
2. `_la_red_hd_-_gattag`
3. `_del_cannon._person`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (476,503 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 144,217 |
| Total Tokens | 7,040,353 |
| Mean Frequency | 48.82 |
| Median Frequency | 4 |
| Frequency Std Dev | 2201.90 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 519,158 |
| 2 | l | 332,263 |
| 3 | la | 287,692 |
| 4 | del | 200,975 |
| 5 | è | 195,911 |
| 6 | a | 181,605 |
| 7 | el | 167,836 |
| 8 | e | 158,973 |
| 9 | in | 125,242 |
| 10 | che | 81,914 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | platamone | 2 |
| 2 | ludvik | 2 |
| 3 | zorzut | 2 |
| 4 | alojz | 2 |
| 5 | gradnik | 2 |
| 6 | böhmstetten | 2 |
| 7 | monegasche | 2 |
| 8 | diaconești | 2 |
| 9 | chichinsci | 2 |
| 10 | şerbănești | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0675 |
| R² (Goodness of Fit) | 0.999638 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 54.0% |
| Top 1,000 | 72.1% |
| Top 5,000 | 82.9% |
| Top 10,000 | 87.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9996 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 54.0% of corpus
- **Long Tail:** 134,217 words needed for remaining 12.7% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8136 | 0.3373 | N/A | N/A |
| **mono_64d** | 64 | 0.7985 | 0.2665 | N/A | N/A |
| **mono_128d** | 128 | 0.7531 | 0.2072 | N/A | N/A |
| **aligned_32d** | 32 | 0.8136 🏆 | 0.3393 | 0.0920 | 0.3580 |
| **aligned_64d** | 64 | 0.7985 | 0.2646 | 0.1660 | 0.5380 |
| **aligned_128d** | 128 | 0.7531 | 0.2006 | 0.2320 | 0.5780 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8136 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2693. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 23.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.446** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-s` | suldà, sedimm, serraj |
| `-a` | alfanumerich, antiege, apinac |
| `-c` | capitana, centralizzazzion, concentrich |
| `-p` | percepìd, pròssima, pizzà |
| `-ca` | capitana, cabardes, cambo |
| `-b` | beve, broeulla, buildings |
| `-m` | mésage, mysteries, mia |
| `-d` | dificila, dàl, dreits |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | capitana, ghiffa, vallinfreda |
| `-n` | granon, repulsion, eisenbahn |
| `-e` | beve, antiege, häme |
| `-i` | liebenbergii, percassi, kiuruvesi |
| `-o` | riuso, malvito, quagliuzzo |
| `-s` | vachères, mysteries, mauvais |
| `-t` | nètt, tunet, fònoisolant |
| `-on` | granon, repulsion, centralizzazzion |

### 6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

| Stem | Cohesion | Substitutability | Examples |
|------|----------|------------------|----------|
| `zzio` | 2.50x | 36 contexts | azzion, lazzio, dozzion |
| `rovi` | 2.01x | 57 contexts | rovin, rovid, trovi |
| `itan` | 1.73x | 84 contexts | titan, ritan, gaitan |
| `stre` | 1.63x | 106 contexts | èstre, stret, strel |
| `lter` | 1.80x | 61 contexts | òlter, älter, olter |
| `ifer` | 1.85x | 49 contexts | cifer, zifer, riferì |
| `inci` | 1.56x | 98 contexts | vinci, incis, incin |
| `perf` | 1.94x | 39 contexts | perfet, perfid, perfèt |
| `popo` | 2.31x | 21 contexts | popoi, popoj, popov |
| `istr` | 1.57x | 93 contexts | istra, nistra, distro |
| `omun` | 2.09x | 29 contexts | comun, comune, comunn |
| `tret` | 2.23x | 23 contexts | stret, trets, strett |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-c` | `-a` | 182 words | consideràda, calabiana |
| `-s` | `-a` | 140 words | satyagraha, südtirulesa |
| `-p` | `-a` | 135 words | porta, provenienza |
| `-a` | `-a` | 96 words | apiifolia, ajaa |
| `-c` | `-o` | 79 words | collecchio, cosimo |
| `-c` | `-e` | 77 words | cadore, cunoniaceae |
| `-s` | `-n` | 74 words | stagion, stallikon |
| `-c` | `-n` | 74 words | cardinalin, cunserven |
| `-d` | `-a` | 71 words | diavolezza, dulia |
| `-b` | `-a` | 64 words | bicicleta, balaustra |

### 6.5 Recursive Morpheme Segmentation

Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| independentisem | **`independentis-e-m`** | 7.5 | `e` |
| büsserach | **`büsser-a-ch`** | 7.5 | `a` |
| desvilupar | **`desvilup-a-r`** | 7.5 | `a` |
| sudcorean | **`sudco-re-an`** | 7.5 | `re` |
| ingrendient | **`ingrendi-e-nt`** | 7.5 | `e` |
| desgrazzia | **`de-s-grazzia`** | 7.5 | `grazzia` |
| monterrei | **`monterr-e-i`** | 7.5 | `e` |
| beutelsbach | **`beutelsb-a-ch`** | 7.5 | `a` |
| pianzanda | **`pianza-n-da`** | 7.5 | `n` |
| compagnii | **`compagn-i-i`** | 7.5 | `i` |
| marchesan | **`marches-a-n`** | 7.5 | `a` |
| scrivania | **`scriva-n-ia`** | 7.5 | `n` |
| recustrüii | **`recustrü-i-i`** | 7.5 | `i` |
| principiar | **`princip-ia-r`** | 6.0 | `princip` |
| modernitaa | **`moderni-ta-a`** | 6.0 | `moderni` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lombard shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (3.47x) |
| N-gram | **2-gram** | Lowest perplexity (268) |
| Markov | **Context-4** | Highest predictability (94.2%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 11:37:13*